We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1（u^mi）xixi in R^n × （O,∞）, where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{...We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1（u^mi）xixi in R^n × （O,∞）, where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{mi}≤ 1, ∑i^n=1 mi 〉 n - 2, and max1≤i≤n{mi} ≤1/n（2 ＋ ∑i^n=1 mi）.展开更多
We study some classes of functions satisfying the assumptions similar to but weaker than those for the classical B2 function classes used in the research of quasi-linear parabolic equations as well as the ones used in...We study some classes of functions satisfying the assumptions similar to but weaker than those for the classical B2 function classes used in the research of quasi-linear parabolic equations as well as the ones used in the research of degenerate parabolic equations including porous medium equations. Consequently, we prove that a function in such a class is continuous. As an application, we obtain the estimate for the continuous modulus of the solutions of a few degenerate parabolic equations in divergence form, including the anisotropic porous equations.展开更多
基金The research is supported by National 973-Project the Trans-Century Training Programme Foundation for the Talents by the Ministry of Education
文摘We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1（u^mi）xixi in R^n × （O,∞）, where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{mi}≤ 1, ∑i^n=1 mi 〉 n - 2, and max1≤i≤n{mi} ≤1/n（2 ＋ ∑i^n=1 mi）.
基金This work was partially supported by the University of Nancy Iby National 973-Project from MOST as well as well Trans-Century Training Programme Foundation for the Talents by Ministry of Education
文摘We study some classes of functions satisfying the assumptions similar to but weaker than those for the classical B2 function classes used in the research of quasi-linear parabolic equations as well as the ones used in the research of degenerate parabolic equations including porous medium equations. Consequently, we prove that a function in such a class is continuous. As an application, we obtain the estimate for the continuous modulus of the solutions of a few degenerate parabolic equations in divergence form, including the anisotropic porous equations.
